CN110568497B - Accurate solving method for seismic first-motion wave travel time under complex medium condition - Google Patents

Accurate solving method for seismic first-motion wave travel time under complex medium condition Download PDF

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CN110568497B
CN110568497B CN201910917119.8A CN201910917119A CN110568497B CN 110568497 B CN110568497 B CN 110568497B CN 201910917119 A CN201910917119 A CN 201910917119A CN 110568497 B CN110568497 B CN 110568497B
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CN110568497A (en
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乔宝平
雷宇航
贺伟光
潘自强
曹成寅
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Beijing Research Institute of Uranium Geology
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    • G01V1/00—Seismology; Seismic or acoustic prospecting or detecting
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Abstract

The invention belongs to the field of acquisition and processing of seismic data in a well or on the earth, and particularly relates to a method for accurately solving seismic first-motion wave travel time under a complex medium condition, which comprises the following steps: mesh subdivision is carried out on the slowness model of the medium, wherein constant medium model parameters are arranged inside each unit mesh, and the first-motion waves to be solved are positioned at the intersection points of the unit meshes during traveling; step two: initializing, giving a constant slowness value inside each unit grid, and establishing a slowness model s (x); step three: calculating a travel time factorization factor tau (x) and a slowness model factorization factor alpha (x); step four: carrying out iterative calculation of the first-motion wave travel time T (x) from four directions; step five: in the first-motion wave travel time calculation of each direction, the following calculation is carried out for each grid node; step six: and repeating the fourth step and the fifth step until the infinite norm of the first-motion wave traveling time is less than 1E-6s, and obtaining a result, namely the first-motion wave traveling time field under the complex medium condition.

Description

Accurate solving method for seismic first-motion wave travel time under complex medium condition
Technical Field
The invention belongs to the field of acquisition and processing of seismic data in a well or on the earth surface, and particularly relates to an accurate solution method for seismic first-motion wave travel time under a complex medium condition.
Background
With the continuous progress of seismic exploration technology, the pre-stack full-waveform inversion technology is also continuously developed, and in order to obtain a more accurate inversion result, a reliable initial parameter model is often required to be provided. The seismic tomography inversion can analyze layer by layer to invert the internal structure of the earth, obtain the internal fine structure and physical parameters, and provide a reliable initial model for full waveform inversion. The forward numerical simulation calculation based on the equation of an equation is a key step of tomography, and the precision and the speed of the forward numerical simulation calculation are directly related to the resolution and the reliability of the tomography inversion. Although the classical equation solving method based on ray tracing has high calculation speed and can intuitively reflect the geometric propagation path of seismic waves, the classical equation solving method has difficulty in processing media with strong speed change and solving the global minimum travel time, and has ray shadow regions, so that the method cannot meet the accurate solution of the equation under the condition of complex media. The finite difference approximate solution function method based on the extended wavefront has the advantages of high calculation efficiency, no blind area and the like, but under the condition of a complex medium, the local stability of the method needs to be improved, and the real global minimum travel time solution cannot be obtained. In order to solve the problems, a fast scanning algorithm based on factorization is developed, so that the stability of the algorithm is guaranteed, and the singularity of the solution at the seismic source point is well solved. But the accurate solution of the near-field solution and the far-field solution can not be ensured at the same time, so that the application effect of the seismic tomography inversion in the accurate exploration of a complex geological target body is restricted. Therefore, there is still a need to develop an accurate solution for seismic first-arrival wave travel under complex medium conditions, which solves the above-mentioned deficiencies of the prior art.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides an accurate solution method for seismic first-motion wave traveling under a complex medium condition, which is used for realizing self-adaptive accurate calculation of seismic first-motion wave traveling.
The technical scheme of the invention is as follows:
an accurate solving method for seismic first-motion wave travel under a complex medium condition comprises the following steps:
the method comprises the following steps: mesh subdivision is carried out on the slowness model of the medium, wherein constant medium model parameters are arranged inside each unit mesh, and the first-motion waves to be solved are positioned at the intersection points of the unit meshes during traveling;
step two: initializing, giving a constant slowness value inside each unit grid, and establishing a slowness model s (x);
step three: calculating a travel time factorization factor tau (x) and a slowness model factorization factor alpha (x);
step four: carrying out iterative calculation of the first-motion wave travel time T (x) from four directions;
step five: in the first-motion wave travel time calculation of each direction, the following calculation is carried out for each grid node;
step six: and repeating the fourth step and the fifth step until the infinite norm of the first-motion wave traveling time is less than 1E-6s, and obtaining a result, namely the first-motion wave traveling time field under the complex medium condition.
The second step further includes: and giving the travel time of the first arrival wave at the seismic source point as 0 and the travel time of other grid intersections as a maximum value, and establishing an initialized travel time field T (x).
Step three further comprises as described above: establishing a uniform slowness model s0(x) Its value is the slowness value at the seismic source point; by T0(x)＝r(x)*s0(x) Calculating a first-arrival travel time field under a uniform slowness model, wherein r (x) is the distance from a seismic source point to any point in a medium; then, a factorization formula is utilized to obtain a factorization factor tau (x) and a slowness model factorization factor alpha (x) during travel, wherein the formula is as follows:
s(x)＝s0(x)α(x)；T(x)＝T0(x)τ(x)
when T is0(x) When 0, τ (x) is s (x).
Where x represents spatial coordinates, s (x) represents a slowness model, s0(x) Representing a uniform slowness model with the value of slowness at the seismic source point, α (x) representing a slowness model decomposition factor, τ (x) representing a travel time field decomposition factor, T (x) representing a travel time field sought under a slowness model s (x), T0(x) Representing the uniform slowness model s0(x) The calculated travel time field is then generated.
The four directions in the fourth step include as described above:
the first direction is as follows: from the upper left direction to the lower right direction, i.e.: i is 1: NX; j is 1: NZ
The second direction is as follows: from the upper right direction to the lower left direction, i.e.: 1, i ═ NX; j is 1: NZ
The third direction: from the lower right direction to the upper left direction, i.e.: 1, i ═ NX; j equals NZ:1
The direction is four: from the lower left direction to the upper right direction, i.e.: i is 1: NX; j equals NZ:1
Wherein i and j represent grid node coordinates after uniform discretization in the x and z directions respectively; NX and NZ represent the number of grid nodes in the x and z directions, respectively.
Step five further includes as described above:
calculating spherical wave first arrival travel time T at grid node by using four-point differential spherical wave operatorS(x) The formula is:
TS(x)＝T0(x)τ(x)
Figure BDA0002216509070000031
Figure BDA0002216509070000032
Figure BDA0002216509070000033
Figure BDA0002216509070000034
τi＝τi-1,j-τi,j-1+τi-1,j-1
τj＝τi,j-1-τi-1,j+τi-1,j-1
wherein h isiAnd hjSpatial sampling intervals in the x and z directions are represented, respectively; tau isi,jRepresents the time value, τ, at the discrete grid node (i, j)0,iAnd τ0,jRespectively represent tau0(x) The directional derivatives in the x and z directions, TS(x) Representing the travel time of the first-motion wave obtained by the four-point difference spherical wave operator, a, b and c respectively represent a quadratic term, a first-order term and a constant term coefficient of a unary quadratic equation with an independent variable of tau (x).
Step five further includes as described above: calculating plane wave first arrival travel time T at grid nodes by using four-point differential plane wave operatorP(x) The formula is:
Figure BDA0002216509070000041
Figure BDA0002216509070000042
Figure BDA0002216509070000043
Figure BDA0002216509070000044
Ti＝Ti-1,j-Ti,j-1+Ti-1,j-1
Tj＝Ti,j-1-Ti-1,j+Ti-1,j-1
wherein h isiAnd hjSpatial sampling intervals in the x and z directions are represented, respectively; t isi,jRepresents the time value, T, at a discrete grid node (i, j)P(x) Representing the first-motion travel time calculated by the four-point differential plane wave operator.
Step five further includes as described above: calculating the first-motion travel time T of the direct wave (or refracted wave) propagating along the grid interface by using a two-point difference operatorR(x) The formula is:
Figure BDA0002216509070000045
TR(x)＝min(Th(x),Tv(x))
Th(x)＝hi min(sd(x),su(x))
Tv(x)＝hj min(sl(x),sr(x))
wherein h isiAnd hjSpatial sampling intervals in the x and z directions are represented, respectively; t ish(x) And Tv(x) S represents the travel of a direct wave (or refracted wave) propagating in the horizontal and vertical directions, respectivelyu(x) And sd(x) Respectively represents the slowness values, s, of the upper and lower grids of the direct wave (or refracted wave) propagation interfacel(x) And sr(x) Respectively representing the slowness values of the left grid and the right grid of the propagation interface of the direct wave (or the refracted wave), the function min (a, b) represents the smaller value of the selected a and b, and TR(x) Representing the first-motion wave travel time obtained by the two-point difference operator;
adaptively selecting and updating a first-arrival travel time field T (x) and a travel time field decomposition factor tau (x), wherein the formula is as follows:
Tupdate(x)＝min(min(T(x),TR(X)),min(TS(x),TP(x)))
if(Tupdate(x)＜T(x))
Figure BDA0002216509070000051
wherein, TR(x) Representing the first-motion travel time T obtained by a two-point difference operatorP(x) Representing the first-arrival travel time, T, calculated by the four-point differential plane wave operatorS(x) Representing the first arrival travel time, T, calculated by four-point differential spherical wave operatorupdate(x) Representing the time of the sought trip to be updated.
The invention has the beneficial effects that:
the invention designs an accurate solving method for seismic first-arrival wave travel under the complex medium condition, which fully combines the respective advantages of a spherical wave operator and a plane wave operator, and can realize the accurate solving of an equation of a first-arrival wave of a near field and a far field in a self-adaptive manner on the basis of the Fermat principle.
Drawings
FIG. 1 is a schematic diagram of finite difference mesh subdivision in an accurate solution method for seismic first-motion wave traveling under a complex medium condition, which is designed by the invention;
FIG. 2 is a schematic diagram of a four-point difference operator in an accurate solution method for seismic first-motion wave travel under a complex medium condition according to the present invention;
FIG. 3 is a schematic diagram of two-point difference operators in an accurate solution method for seismic first-motion wave travel under a complex medium condition according to the present invention;
FIG. 4 is a Marmousi model with complex media features;
FIG. 5 is an isochronous curve of a first-arrival travel time field under a Marmousi model with complex medium characteristics according to the present invention;
Detailed Description
The invention will be further described with reference to the following figures and examples: an accurate solving method for seismic first-motion wave travel under a complex medium condition comprises the following steps:
the method comprises the following steps: mesh subdivision is carried out on the slowness model of the medium, wherein constant medium model parameters are arranged inside each unit mesh, and the first-motion waves to be solved are positioned at the intersection points of the unit meshes during traveling; as indicated by the open circles in fig. 1.
Step two: initializing, giving a constant slowness value inside each unit grid, and establishing a slowness model s (x);
step three: calculating a travel time factorization factor tau (x) and a slowness model factorization factor alpha (x);
step four: carrying out iterative calculation of the first-motion wave travel time T (x) from four directions;
step five: in the first-motion wave travel time calculation of each direction, the following calculation is carried out for each grid node;
step six: and repeating the fourth step and the fifth step until the infinite norm of the first-motion wave traveling time is less than 1E-6s, and obtaining a result, namely the first-motion wave traveling time field under the complex medium condition.
The second step further includes: and giving the travel time of the first arrival wave at the seismic source point as 0 and the travel time of other grid intersections as a maximum value, and establishing an initialized travel time field T (x).
Step three further comprises as described above: establishing a uniform slowness model s0(x) Its value is the slowness value at the seismic source point; by T0(x)＝r(x)*s0(x) Calculating a first-arrival travel time field under a uniform slowness model, wherein r (x) is the distance from a seismic source point to any point in a medium; then, a factorization formula is utilized to obtain a factorization factor tau (x) and a slowness model factorization factor alpha (x) during travel, wherein the formula is as follows:
s(x)＝s0(x)α(x)；T(x)＝T0(x)τ(x)
when T is0(x) When 0, τ (x) is s (x).
Where x represents spatial coordinates, s (x) represents a slowness model, s0(x) Representing a uniform slowness model with the value of slowness at the seismic source point, α (x) representing a slowness model decomposition factor, τ (x) representing a travel time field decomposition factor, T (x) representing a travel time field sought under a slowness model s (x), T0(x) Representing the uniform slowness model s0(x) The calculated travel time field is then generated.
The four directions in the fourth step include as described above:
the first direction is as follows: from the upper left direction to the lower right direction, i.e.: i is 1: NX; j is 1: NZ
The second direction is as follows: from the upper right direction to the lower left direction, i.e.: 1, i ═ NX; j is 1: NZ
The third direction: from the lower right direction to the upper left direction, i.e.: 1, i ═ NX; j equals NZ:1
The direction is four: from the lower left direction to the upper right direction, i.e.: i is 1: NX; j equals NZ:1
Wherein i and j represent grid node coordinates after uniform discretization in the x and z directions respectively; NX and NZ represent the number of grid nodes in the x and z directions, respectively.
Step five further includes as described above:
calculating spherical wave first arrival travel time T at grid node by using four-point differential spherical wave operatorS(x) The formula is:
TS(x)＝T0(x)τ(x)
Figure BDA0002216509070000071
Figure BDA0002216509070000072
Figure BDA0002216509070000073
Figure BDA0002216509070000074
τi＝τi-1,j-τi,j-1+τi-1,j-1
τj＝τi,j-1-τi-1,j+τi-1,j-1
wherein h isiAnd hjSpatial sampling intervals in the x and z directions are represented, respectively; tau isi,jRepresents the time value, τ, at the discrete grid node (i, j)0,iAnd τ0,jRespectively represent tau0(x) The directional derivatives in the x and z directions, TS(x) Representing the travel time of the first-motion wave obtained by the four-point difference spherical wave operator, a, b and c respectively represent a quadratic term, a first-order term and a constant term coefficient of a unary quadratic equation with an independent variable of tau (x).
Fig. 2 shows a four-point difference operator, where the filled circles in fig. 2 represent known first-arrival wave travel of mesh nodes, and the empty circles represent first-arrival wave travel of mesh nodes to be solved.
The fifth step further comprises: calculating plane wave first arrival travel time T at grid nodes by using four-point differential plane wave operatorP(x) The formula is:
Figure BDA0002216509070000081
Figure BDA0002216509070000082
Figure BDA0002216509070000083
Figure BDA0002216509070000084
Ti＝Ti-1,j-Ti,j-1+Ti-1,j-1
Tj＝Ti,j-1-Ti-1,j+Ti-1,j-1
wherein h isiAnd hjSpatial sampling intervals in the x and z directions are represented, respectively; t isi,jRepresents the time value, T, at a discrete grid node (i, j)P(x) Representing the first-motion travel time calculated by the four-point differential plane wave operator.
Step five further includes as described above: calculating the first-motion travel time T of the direct wave (or refracted wave) propagating along the grid interface by using a two-point difference operatorR(x) The formula is:
Figure BDA0002216509070000085
TR(x)＝min(Th(x),Tv(x))
Th(x)＝hi min(sd(x),su(x))
Tv(x)＝hj min(sl(x),sr(x))
wherein h isiAnd hjSpatial sampling intervals in the x and z directions are represented, respectively; t ish(x) And Tv(x) S represents the travel of a direct wave (or refracted wave) propagating in the horizontal and vertical directions, respectivelyu(x) And sd(x) Respectively represents the slowness values, s, of the upper and lower grids of the direct wave (or refracted wave) propagation interfacel(x) And sr(x) Respectively representing the slowness values of the left grid and the right grid of the propagation interface of the direct wave (or the refracted wave), the function min (a, b) represents the smaller value of the selected a and b, and TR(x) Representing the first-motion wave travel time obtained by the two-point difference operator; fig. 3 shows a two-point difference operator, where the solid circles represent the known first-arrival wave travel of the mesh nodes, and the hollow circles represent the first-arrival wave travel of the mesh nodes to be obtained.
Adaptively selecting and updating a first-arrival travel time field T (x) and a travel time field decomposition factor tau (x), wherein the formula is as follows:
Tupdate(x)＝min(min(T(x),TR(X)),min(TS(x),TP(x)))
if(Tupdate(x)＜T(x))
Figure BDA0002216509070000091
wherein, TR(x) Representing the first-motion travel time T obtained by a two-point difference operatorP(x) Representing the first-arrival travel time, T, calculated by the four-point differential plane wave operatorS(x) Representing the first arrival travel time, T, calculated by four-point differential spherical wave operatorupdate(x) Representing the time of the sought trip to be updated.
Fig. 4 shows a Marmousi model with drastic changes in longitudinal and lateral velocities, which can be seen in various complex geological formations. On the basis of the model, the first arrival wave travel time field is calculated by using the steps from one to six, and the result is shown in fig. 5, and an isochronal curve conforming to the wave field propagation characteristics can be seen.
The method for accurately solving the seismic first-motion wave travel time under the complex medium condition is not limited to the above embodiment, and other embodiments obtained by those skilled in the art according to the technical solution of the present invention satisfy the principle of the present invention, and also belong to the technical innovation scope of the present invention.

Claims (6)

1. An accurate solving method for seismic first-motion wave travel under a complex medium condition is characterized by comprising the following steps:
the method comprises the following steps: mesh subdivision is carried out on the slowness model of the medium, wherein constant medium model parameters are arranged inside each unit mesh, and the first-motion waves to be solved are positioned at the intersection points of the unit meshes during traveling;
step two: initializing, giving a constant slowness value inside each unit grid, and establishing a slowness model s (x);
step three: calculating a travel time factorization factor tau (x) and a slowness model factorization factor alpha (x);
step four: carrying out iterative calculation of the first-motion wave travel time T (x) from four directions;
step five: in the first-motion wave travel time calculation of each direction, the following calculation is carried out for each grid node; calculating spherical wave first arrival travel time T at grid node by using four-point differential spherical wave operatorS(x) The formula is:
TS(x)＝T0(x)τ(x)
Figure FDA0003086173050000011
Figure FDA0003086173050000012
Figure FDA0003086173050000013
Figure FDA0003086173050000014
τi＝τi-1,j-τi,j-1+τi-1,j-1
τj＝τi,j-1-τi-1,j+τi-1,j-1
wherein h isiAnd hjSpatial sampling intervals in the x and z directions are represented, respectively; tau isi,jRepresents the time value, T, at a discrete grid node (i, j)0,iAnd T0,jRespectively represent tau0(x) The directional derivatives in the x and z directions, TS(x) Representing the traveling of the first-motion wave obtained by a four-point differential spherical wave operator, wherein a, b and c respectively represent a quadratic term, a first-order term and a constant term coefficient of a unary quadratic equation with an independent variable of tau (x); s0(x) Representing a uniform slowness model, and the value of the uniform slowness model is a slowness value at the seismic source point; t is0(x) Representing the uniform slowness model s0(x) The calculated travel time field is downloaded;
step six: and repeating the fourth step and the fifth step until the infinite norm of the first-motion wave traveling time is less than 1E-6s, and obtaining a result, namely the first-motion wave traveling time field under the complex medium condition.
2. The method for accurately solving the seismic first-motion wave travel time under the complex medium condition as claimed in claim 1, wherein: the second step further comprises: and giving the travel time of the first arrival wave at the seismic source point as 0 and the travel time of other grid intersections as a maximum value, and establishing an initialized travel time field T (x).
3. The method for accurately solving the seismic first-motion wave travel time under the complex medium condition as claimed in claim 2, wherein: the third step further comprises: establishing a uniform slowness model s0(x) Its value is the slowness value at the seismic source point; by T0(x)＝r(x)*s0(x) Calculating a first-arrival travel time field under a uniform slowness model, wherein r (x) is the distance from a seismic source point to any point in a medium; then, using a factorization formula to solve tau (x) and alpha (x), wherein the solving formula is as follows:
s(x)＝s0(x)α(x)；T(x)＝T0(x)τ(x)
when T is0(x) When 0, τ (x) is s (x);
where x represents spatial coordinates, s (x) represents a slowness model, s0(x) Representing a uniform slowness model with the value of slowness at the seismic source point, α (x) representing a slowness model decomposition factor, τ (x) representing a travel time field decomposition factor, T (x) representing a travel time field sought under a slowness model s (x), T0(x) Representing a uniform slowness models0(x) The calculated travel time field is then generated.
4. The method for accurately solving the seismic first-motion wave travel time under the complex medium condition as claimed in claim 3, wherein: the four directions in the step four comprise:
the first direction is as follows: i is 1: NX; NZ, propagating from the upper left direction to the lower right direction;
the second direction is as follows: 1, i ═ NX; NZ, propagating from the upper right direction to the lower left direction;
the third direction: 1, i ═ NX; 1, from the lower right direction to the upper left direction;
the direction is four: i is 1: NX; 1, propagating from a lower left direction to an upper right direction;
wherein i and j represent grid node coordinates after uniform discretization in the x and z directions respectively; NX and NZ represent the number of grid nodes in the x and z directions, respectively.
5. The method for accurately solving the seismic first-motion wave travel time under the complex medium condition as claimed in claim 4, wherein: the fifth step further comprises: calculating plane wave first arrival travel time T at grid nodes by using four-point differential plane wave operatorP(x) The formula is:
Figure FDA0003086173050000031
Figure FDA0003086173050000032
Figure FDA0003086173050000033
Figure FDA0003086173050000034
Ti＝Ti-1,j-Ti,j-1+Ti-1,j-1
Tj＝Ti,j-1-Ti-1,j+Ti-1,j-1
wherein h isiAnd hjSpatial sampling intervals in the x and z directions are represented, respectively; t isi,jRepresents the time value, T, at a discrete grid node (i, j)P(x) Representing the first-motion travel time calculated by the four-point differential plane wave operator.
6. The method for accurately solving the seismic first-motion wave travel time under the complex medium condition as claimed in claim 5, wherein: the fifth step further comprises: calculating the first arrival travel time T of the direct wave propagating along the grid interface by using a two-point difference operatorR(x) The formula is:
Figure FDA0003086173050000041
TR(x)＝min(Th(x),Tv(x))
Th(x)＝hi min(sd(x),su(x))
Tv(x)＝hj min(sl(x),sr(x))
wherein h isiAnd hjSpatial sampling intervals in the x and z directions are represented, respectively; t ish(x) And Tv(x) Representing travel times, s, of direct waves propagating in the horizontal and vertical directions, respectivelyu(x) And sd(x) Respectively represents the slowness values, s, of the upper and lower grids of the direct wave propagation interfacel(x) And sr(x) Respectively representing the slowness values of the left and right grids of the direct wave propagation interface, the function min (a, b) represents the smaller value of the selected a and b, and TR(x) Representing the first-motion wave travel time obtained by the two-point difference operator;
adaptively selecting and updating a first-arrival wave travel time field T (x) and a decomposition factor tau (x), wherein the formula is as follows:
Tupdate(x)＝min(min(T(x),TR(X)),min(TS(x),TP(x)))
if(Tupdate(x)＜T(x))
Figure FDA0003086173050000042
wherein, TR(x) Representing the first-motion travel time T obtained by a two-point difference operatorP(x) Representing the first-arrival travel time, T, calculated by the four-point differential plane wave operatorS(x) Representing the first arrival travel time, T, calculated by four-point differential spherical wave operatorupdate(x) When representing the sought journey to be updated, T0(x) Representing the uniform slowness model s0(x) The calculated travel time field is then generated.
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